1. Field of the Invention
This invention relates to navigation, and more particularly to techniques for augmenting navigation with measurements of Near Earth Objects (NEOs).
2. Description of the Related Art
Long-range navigation such as for satellites, aircraft or missiles is commonly accomplished by providing an initial position, velocity and acceleration (“PVA”) and attitude, using inertial sensors on-board the platform to provide inertial measurements and integrating those measurements to update a navigation PVA and attitude over time. The inertial measurements may be provided by acceleration and angular rate sensors, which may be provided in an Inertial Measurement Unit or IMU. The navigation PVA and attitude include an error component that is bounded by an uncertainty region. The uncertainty region is dependent on several factors including the accuracy of the initial PVA and attitude, the quality of the inertial sensors (which tend to drift over time), and the accuracy of the clock. Without correction, the uncertainty region of the navigation PVA will continue to grow over time.
A Kalman Filter is typically used to reduce the noise and some of the bias errors in the integrator's estimate of PVA. The noise reduction and bias corrections a Kalman Filter provides are limited to the errors that are observable with the platform's IMU and a priori knowledge of the platform's dynamics in the form of a “motion model”. Kalman filtering reduces but does not eliminate the growth in the uncertainty region.
One option to improve the navigation accuracy is to use very high precision (and high cost) inertial sensors that exhibit minimal drift over time. The integrated error remains low and external correction is unnecessary. An example of this approach is found in the Minute Man Missile. Due to the high cost of the inertial sensors this approach is not viable for many platforms.
In some systems gyroscopes are utilized to directly measure attitude. This also simplifies the integration and position estimation process. Star sighting is also used to correct attitude. This technique is passive in the sense that no information passes from the star to the platform. The platform obtains the required information through the use of internal instrumentation, typically a stellar camera or telescope. An example of a star sighting augmentation is found in the Trident Missile system.
The inertial navigation system can be augmented with other instrumentation or measurements to periodically correct the navigation PVA. GPS is often used to augment inertial navigation systems. GPS is an active system in that GPS requires data to be actively sent from an external source (GPS satellites) to a receiver on the vehicle. The GPS signals can be used to provide external measurement, separate from the internal measurement system, of true position and velocity. These are in turn provided as inputs to the Kalman Filter to correct the inertial position estimates. The active transfer of data form the GPS system to the platform is often seen as a significant limitation. Many platforms must be designed and rated to operate in a GPS denied environment.
Another technique uses celestial (star) navigation to provide a correction to latitude and longitude if the altitude is precisely known. The drawbacks to celestial navigation are that the altitude must be precisely known in order to correct position and that the error in the correction itself is at best 1 km due to the extreme distances to the stars and the difficulty in obtaining a precise altitude measurement.
Another technique to augment navigation PVA and attitude uses inertial measurements combined with near earth object (NEO) sightings. NEOs are typically other Earth-orbiting satellites, and thus are much closer to the platform than stars. The Kalman filter states are extended to include the bearings to some number of NEO's. The inclusion of the NEO data in the Kalman filter improves the accuracy of the navigation PVA and attitude. This technique described in Long Duration Strapdown Stellar-Inertial Navigation Using Satellite Tracking, A. Brown et. al., IEEE 1992 requires a large number of NEO sightings over a long period of time to improve the accuracy of the navigation PVA and attitude.
This approach depends on tracking the NEOs relative to inertial space. The Kalman filter develops and updates its track estimates using angle observations from an onboard stellar camera, and ephemeris orbit data for the NEO's. The Kalman filter is fed the on-board inertial measurement data, the stellar camera data, and the NEO orbital parameters and predicts the platform's navigation PVA and attitude and the NEO positions.
Filter convergence is achieved only after there is sufficient time to observe the motion of the NEOs in their orbits. In effect the technique requires sufficient time to compare the predicted or modeled motion of the NEO positions with the observed data. As each new observation is made this comparison is used to update the motion model of the NEO and platform's PVA and attitude data. When the model prediction and the observations agree within a prescribed amount the filter is said to have converged.
The Kalman filter predicts the variance in the PVA and attitude estimates. The variance estimates are a measure of how well the model prediction agrees with the observed data, and is therefore the standard measure used to determine convergence. Experiments with these methods show that the Kalman filter requires at least several minutes, often 30 minutes to hours, to converge to obtain a precision correction. A further limitation seen in these experiments was the apparent requirement to restrict the acceleration or turns of the platform while the Kalman filter converges.